This article presents a novel path-following algorithm for fixed-wing unmanned aerial vehicles by virtue of a nonlinear optimal control approach and wind disturbance observers. Different from some exiting algorithms, the proposed algorithm formulates the path-following problem into a control problem by introducing auxiliary dynamics for the path parameter. The proposed controller is designed in an optimal and systematic manner where the control action is generated according to a well-defined cost function. This framework does not require any complex geometric coordinate transformation and can be easily tuned to accommodate curved reference paths, making it straightforward to deploy in different flight missions. Moreover, the wind influences on the path-following performance is explicitly compensated by the proposed algorithm based on the wind estimates provided by nonlinear disturbance observers. The closed-loop stability, including the auxiliary dynamics for path parameter and observer dynamics for wind estimation, is also analyzed. The feasibility and effectiveness of the proposed algorithm have been thoroughly validated in simulation studies and realistic flight tests.